Initially when we developed the site, we activated this plugin and as there were not many posts, the plugin worked fine.

A couple of days ago, I deactivated the plugin and reactivated it the next day.

As I understand, the reactivation of plugin, started the indexing procedure all over again which resulted in heavy load on the server and the server going down for a good 3 hours.

I then eventually had to deactivate the plugin again and now the site is working fine.

I now plan to activate the plugin again by installing the latest version. What I would like to ask is that whether reactivating the plugin again will have any effect on my server? And if yes, then how much time should it take for the whole indexing mechanism to be completed.

Is there any way that I can activate the plugin and not let the server to go down?

No, the deactivation/reactivation should not have triggered a cache flush.

I can't tell you anything about how much time things take, as it's not meant to run as a job... it should grow organically over time. There is info in the FAQ on less computationally intensive options. You can follow those instructions to make the operation faster.